New Algorithms in Rigid-Body Registration and Estimation of Registration Accuracy

Abstract

Rigid-body registration is an important research area with major applications in computer-assisted and image-guided surgery. In these surgeries, often the relationship between the preoperative and intraoperative images taken from a patient must be established. This relationship is computed through a registration process, which finds a set of transformation parameters that maps some point fiducials measured on a patient anatomy to a preoperative model. Due to point measurement error caused by medical measurement instruments, the estimated registration parameters are imperfect and this reduces the accuracy of the performed registrations. Medical measurement instruments often perturb the collected points from the patient anatomy by heterogeneous noise. If the noise characteristics are known, they can be incorporated in the registration algorithm in order to more reliably and accurately estimate the registration parameters and their variances.

Current techniques employed in rigid-body registration are primarily based on the well-known Iterative Closest Points (ICP) algorithm. Such techniques are susceptible to the existence of noise in the data sets, and are also very sensitive to the initial alignment errors. Also, the literature offers no analytical solution on how to estimate the accuracy of the performed registrations in the presence of heterogenous noise.

In an effort to alleviate these problems, we propose and validate various novel registration techniques based on the Unscented Kalman Filter (UKF) algorithm. This filter is generally employed for analyzing nonlinear systems corrupted by additive heterogenous Gaussian noise. First, we propose a new registration algorithm to fit two data sets in the presence of arbitrary Gaussian noise, when the corresponding points between the two data sets are assumed to be known. Next, we extend this algorithm to perform surface-based registration, where point correspondences are not available, but the data sets are roughly aligned. A solution to multi-body point and surface-based registration problem is then proposed based on the UKF algorithm.

The outputs of the proposed UKF registration algorithms are then utilized to estimate the accuracy of the performed registration. For the first time, novel derivations are presented that can estimate the distribution of registration error at a target in the presence of an arbitrary Gaussian noise.